Question

The property appraisal district for Marin County has just installed new software to track residential market values for property tax computations. The manager wants to know the total equivalent cost of all future costs incurred when the three county judges agreed to purchase the software system. If the new system will be used for the indefinite future, find the equivalent value (a) now and (b) for each year hereafter. The system has an installed cost of $2,500,000 and an additional cost of $700,000 at year 8. The annual software maintenance contract cost is $75,000 for the first 4 years, $100,000 for the second 4 years, $125,000 for the third 4 years, and $125,000 thereafter. In addition, there is expected to be a recurring major upgrade cost of $100,000 every 14 years. Assume that i= 7% per year for county funds.

Answer 1

Solution :-

Interest Rate Per Year = 7% per year

Interest Rate of 14 Years = ( 1 + 0.07 )14 - 1 = 1.5785 = 157.85%

Initial Cost = $2,500,000

Present Value of Additional Cost of $700,000 at Year 8 = $700,000 * P/F ( 7% , 8 )

= $700,000 * 0.5820

= $407,400

Now Present value of Annual Software maintenance

Present Value of $75,000 for next 4 Years = $75,000 * P/A ( 7% , 4 ) = $75,000 * 3.387 = $254,025

Present Value of $100,000 for next 4 years = $100,000 * P/A ( 7% , 4 ) * P/F ( 7% , 4 )

= $100,000 * 3.387 * 0.7629 = $258,394.23

Present Value of $125,000 for third 4 years = $125,000 * P/A ( 7% , 4 ) * P/F ( 7% , 8 )

= $125,000 * 3.387 * 0.5820 = $246,404.25

Present Value of Major Upgrade Cost = $100,000 / 157.85% = $63,349.91

( A )

Now Equivalent Value now = $2,500,000 + $407,400 + $254,025 + $258,394.23 + $246,404.25 + $63,349.91

= $3,729,573.39

(B)

Value for Each Year there after = $3,729,573.39 * 7% = $261,070.14

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